As you now have his exact death date you could contact Brent records office to check for burial or cremation details
This definitely looks like the way forward. I tried to find his mother's details, as her death was also registered in Willesden in 1951. No luck. I came to the conclusion that there must be a problem with the records. And on investigation, even though the LB Brent website directs you to Deceased Online, it looks like DO does not hold the records for Willesden New Cemetery - the most likely location.
The only Brent cemeteries named in DO's page for the borough are: Alperton Cemetery, Carpenders Park Cemetery, Willesden Old Burial Ground (St Mary's), and Wembley Old Burial Ground (St John's).
This page gives details of Brent's charges for family history searches, but it doesn't explain how to book one of their six-hour slots:
https://www.brent.gov.uk/births-deaths-marriages-nationality/deaths-and-funeral-services/family-history-searches
